The Friendship Paradox

Feld’s friendship paradox states that ‘your friends have more friends than you, on average’. This paradox arises because extremely popular people, despite being rare, are overrepresented when averaging over friends.

Using a sample of the Twitter firehose, we confirm that the friendship paradox holds for >98% of Twitter users. Because of the directed nature of the follower graph on Twitter, we are further able to confirm more detailed forms of the friendship paradox: everyone you follow or who follows you has more friends and followers than you.This is likely caused by a correlation we demonstrate between Twitter activity, number of friends, and number of followers.

But wait, there’s more..

In addition, we discover two new paradoxes: the virality paradox that states ‘your friends receive more viral content than you, on average’, and the activity paradox, which states ‘your friends are more active than you, on average’. The latter paradox is important in regulating online communication. It may result in users having difficulty maintaining optimal incoming information rates, because following additional users causes the volume of incoming tweets to increase super-linearly. (And this also may relate to why in large complex communities personalized moderation works better than community moderation, as explored in my last blog post).

While users may compensate for increased information flow by increasing their own activity, users become information overloaded when they receive more information than they are able or willing to process. We compare the average size of cascades that are sent and received by overloaded and underloaded users. And we show that overloaded users post and receive larger cascades and they are poor detector of small cascades.

What are the dangers of overload?

Those users who become overloaded, measured by receiving far more incoming messages than they send out, are contending with more tweets than they can handle. Controlling for activity, they are more likely to participate in viral cascades, likely due to receiving the popular cascades multiple times. Any individual tweet’s visibility is greatly diluted for overloaded users, because overloaded users receive so many more tweets than they can handle. Because of the connection between cognitive load and managing information overload, the present results suggest that users will dynamically adjust their social network to maintain some optimal individual level of information flux. (What does this mean for Facebook’s growth?)

Friendship Paradox Redux: Your Friends Are More Interesting Than You – Nathan O. Hodas, Farshad Kooti, Kristina Lerman (PDF of the paper)
http://arxiv.org/abs/1304.3480